Simplify the following expression: $ y = \dfrac{p - 6}{8p - 8} - \dfrac{7}{6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{p - 6}{8p - 8} \times \dfrac{6}{6} = \dfrac{6p - 36}{48p - 48} $ Multiply the second expression by $\dfrac{8p - 8}{8p - 8}$ $ \dfrac{7}{6} \times \dfrac{8p - 8}{8p - 8} = \dfrac{56p - 56}{48p - 48} $ Therefore $ y = \dfrac{6p - 36}{48p - 48} - \dfrac{56p - 56}{48p - 48} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{6p - 36 - (56p - 56) }{48p - 48} $ Distribute the negative sign: $y = \dfrac{6p - 36 - 56p + 56}{48p - 48}$ $y = \dfrac{-50p + 20}{48p - 48}$ Simplify the expression by dividing the numerator and denominator by 2: $y = \dfrac{-25p + 10}{24p - 24}$